How to add reference photos in orthographic view from angles other than the default front, back, top, etc.?
There are two ways (as far as I know)


Add a plane with the texture.
Set the background to the Camera.


1. Add a plane with the texture

This is a way used in a 3D software called MODO.
It is easy to manage the location, rotation and scale.
However it is tedeous and cannot be used in Solid (in matters of viewpoint shading.

There are some tips that can help you with this method.


select "Generate UVs" (on the toolshelf when you made the object)
press the E key (it will resize the uv so that the ratio matches the actual mesh)


2. Set the background to the Camera

Find for "Camera" in the "Axis" of the Background image panel.
This will fix the image as a background image of the camera.

There are some tips that can help you with this method.


lock the location and rotation at the Properties Region
switch between cameras with Ctrl-Numpad0